Castling through an unchecked square

0:00SarahRoger, quick scenario. Tournament hall. You're playing White, your hand is on the king, you're about to castle. And your opponent leans in and asks: has anyone actually checked that square?

0:12RogerAnd nobody has. Which is exactly today's episode: one move, and three different things we might know about one square.

0:20RogerQuick housekeeping first. We're both synthetic voices, the music is generated too, and so is this show. The answers aren't invented, though. Every result you'll hear comes from a recorded Arxo run, and the facts and hashes for each one are in the show notes.

0:37RogerThis is Executable Knowledge: Cases.

0:44RogerChess players learn it early: you don't castle through check. FIDE Laws of Chess, Article 3.8.2: the square the king stands on, the square it crosses, and the square it lands on can't be attacked.

0:59SarahThat part everybody knows.

1:01RogerRight. The tricky part is that little word, not. Not under attack. What does that mean when nobody has looked at the square?

1:10SarahIt means... nobody has looked at the square.

1:14RogerExactly. And that's not the same as nothing there. So we loaded the FIDE rule into Arxo, set up one position, White castling on the king's side, king and rook never moved, and asked the same question three times. Only one thing changes: what the record says about those squares.

1:34SarahCase one.

1:35RogerThe squares were checked, and the record says the square the king has to cross is under attack.

1:42Arxo answerResult: not established.

1:45SarahNot established. So that's a no?

1:47RogerNot quite, and that difference will matter in a minute. It isn't a yes. The rule doesn't grant castling here, and it tells you exactly which condition broke.

1:59Arxo answerBlocker. Required: not — the king's square, the square it must cross, or the square it is to occupy is attacked. Status: refuted.

2:11RogerRefuted. That condition was supposed to hold, and the record says it doesn't: the path is attacked. So the rule won't sign off.

2:21SarahThe path is attacked, so the rule won't sign off. Beginner's book.

2:26RogerBeginner's book. But remember that word: refuted.

2:30SarahCase two.

2:32RogerSame position. The squares were checked, and nothing was found. No attack recorded, no piece in the way.

2:41Arxo answerResult: true. Rule applied: Castling Legal.

2:46SarahThere we go. A yes.

2:47RogerA yes, with eight reasons. Four are plain facts somebody wrote down: White's king, White's rook, White has the move, and White wants to castle with that rook.

2:57RogerThe other four are the interesting ones. The path isn't attacked. There's no piece between the king and the rook. The rook hasn't moved. And the king hasn't moved.

3:11SarahAren't those just facts too?

3:13RogerNobody typed them in. There's no fact saying the path isn't attacked. There's a line saying these squares were checked, and these pieces were checked. The answer marks all four the same way: checked, nothing recorded.

3:28RogerThat's how a not gets earned here. Somebody looked, so an empty record is a clean record.

3:35SarahSo, case three.

3:35RogerCase three is case two with one line deleted. Same board, same pieces, nothing on record about an attack. But nothing says the squares were checked, either.

3:48RogerThat's the tournament hall: hand on the king, and nobody has looked.

3:54Arxo answerResult: not established.

3:57SarahHang on. No attack on record, nothing in the way. Same board as case two. Why isn't it a yes?

4:05RogerSame board, different record. Case two was checked. Case three never was. Listen to the answer this time.

4:14Arxo answerNo blocker. Not refuted — simply no derivation.

4:19RogerNo blocker. Case one had a refuted condition. Here nothing is refuted. Two conditions are simply unknown.

4:27Arxo answerRequired: not — there is a piece between the king and the rook with which castling is to be effected. Status: unknown. Required: not — the king's square, the square it must cross, or the square it is to occupy is attacked. Status: unknown.

4:47SarahSo it's not saying the squares are attacked. And it's not saying they're safe.

4:52RogerRight. It's saying: I don't have that.

4:56RogerThat's the point. A system that reads no attack on file as no attack would wave White straight through. Arxo doesn't. Unknown is not no, and it isn't yes, either.

5:08SarahSo two of the three cases say not established.

5:11RogerFor completely different reasons. In case one, we looked and found a problem. In case three, nobody looked.

5:20SarahWhere else does this bite?

5:22RogerAnywhere a missing record gets read as a clean one. An inspection with no defects recorded: inspected and fine, or never inspected? An audit with no exceptions noted: same question.

5:36RogerArxo keeps those three apart: looked and found a problem, looked and found nothing, never looked.

5:44RogerThree cases, one rule, one square. The facts, the full answers and the hashes are in the show notes. Run them again and you'll get the same three answers.

5:55SarahNext time: another rule, and a few more cases that don't go the way you'd expect.

6:01RogerBoth voices synthetic, every answer from a real run. This was Executable Knowledge: Cases, from Arxo.